/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date:        15. February 2012
* $Revision: 	V1.1.0
*
* Project: 	    CMSIS DSP Library
* Title:	    arm_rfft_f32.c
*
* Description:	RFFT & RIFFT Floating point process function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
*    Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
*    Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
*    Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
*    Documentation updated.
*
* Version 1.0.1 2010/10/05
*    Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
*    Production release and review comments incorporated.
*
* Version 0.0.7  2010/06/10
*    Misra-C changes done
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupTransforms
 */

/**
 * @defgroup RFFT_RIFFT Real FFT Functions
 *
 * \par
 * Complex FFT/IFFT typically assumes complex input and output. However many applications use real valued data in time domain.
 * Real FFT/IFFT efficiently process real valued sequences with the advantage of requirement of low memory and with less complexity.
 *
 * \par
 * This set of functions implements Real Fast Fourier Transforms(RFFT) and Real Inverse Fast Fourier Transform(RIFFT)
 * for Q15, Q31, and floating-point data types.
 *
 *
 * \par Algorithm:
 *
 * <b>Real Fast Fourier Transform:</b>
 * \par
 * Real FFT of N-point is calculated using CFFT of N/2-point and Split RFFT process as shown below figure.
 * \par
 * \image html RFFT.gif "Real Fast Fourier Transform"
 * \par
 * The RFFT functions operate on blocks of input and output data and each call to the function processes
 * <code>fftLenR</code> samples through the transform.  <code>pSrc</code>  points to input array containing <code>fftLenR</code> values.
 * <code>pDst</code>  points to output array containing <code>2*fftLenR</code> values. \n
 * Input for real FFT is in the order of
 * <pre>{real[0], real[1], real[2], real[3], ..}</pre>
 * Output for real FFT is complex and are in the order of
 * <pre>{real(0), imag(0), real(1), imag(1), ...}</pre>
 *
 * <b>Real Inverse Fast Fourier Transform:</b>
 * \par
 * Real IFFT of N-point is calculated using Split RIFFT process and CFFT of N/2-point as shown below figure.
 * \par
 * \image html RIFFT.gif "Real Inverse Fast Fourier Transform"
 * \par
 * The RIFFT functions operate on blocks of input and output data and each call to the function processes
 * <code>2*fftLenR</code> samples through the transform.  <code>pSrc</code>  points to input array containing <code>2*fftLenR</code> values.
 * <code>pDst</code>  points to output array containing <code>fftLenR</code> values. \n
 * Input for real IFFT is complex and are in the order of
 * <pre>{real(0), imag(0), real(1), imag(1), ...}</pre>
 *  Output for real IFFT is real and in the order of
 * <pre>{real[0], real[1], real[2], real[3], ..}</pre>
 *
 * \par Lengths supported by the transform:
 * \par
 * Real FFT/IFFT supports the lengths [128, 512, 2048], as it internally uses CFFT/CIFFT.
 *
 * \par Instance Structure
 * A separate instance structure must be defined for each Instance but the twiddle factors can be reused.
 * There are separate instance structure declarations for each of the 3 supported data types.
 *
 * \par Initialization Functions
 * There is also an associated initialization function for each data type.
 * The initialization function performs the following operations:
 * - Sets the values of the internal structure fields.
 * - Initializes twiddle factor tables.
 * - Initializes CFFT data structure fields.
 * \par
 * Use of the initialization function is optional.
 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
 * To place an instance structure into a const data section, the instance structure must be manually initialized.
 * Manually initialize the instance structure as follows:
 * <pre>
 *arm_rfft_instance_f32 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
 *arm_rfft_instance_q31 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
 *arm_rfft_instance_q15 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
 * </pre>
 * where <code>fftLenReal</code> length of RFFT/RIFFT; <code>fftLenBy2</code> length of CFFT/CIFFT.
 * <code>ifftFlagR</code> Flag for selection of RFFT or RIFFT(Set ifftFlagR to calculate RIFFT otherwise calculates RFFT);
 * <code>bitReverseFlagR</code> Flag for selection of output order(Set bitReverseFlagR to output in normal order otherwise output in bit reversed order);
 * <code>twidCoefRModifier</code> modifier for twiddle factor table which supports 128, 512, 2048 RFFT lengths with same table;
 * <code>pTwiddleAReal</code>points to A array of twiddle coefficients; <code>pTwiddleBReal</code>points to B array of twiddle coefficients;
 * <code>pCfft</code> points to the CFFT Instance structure. The CFFT structure also needs to be initialized, refer to arm_cfft_radix4_f32() for details regarding
 * static initialization of cfft structure.
 *
 * \par Fixed-Point Behavior
 * Care must be taken when using the fixed-point versions of the RFFT/RIFFT function.
 * Refer to the function specific documentation below for usage guidelines.
 */

/*--------------------------------------------------------------------
 *		Internal functions prototypes
 *--------------------------------------------------------------------*/

void arm_split_rfft_f32(
    float32_t* pSrc,
    uint32_t fftLen,
    float32_t* pATable,
    float32_t* pBTable,
    float32_t* pDst,
    uint32_t modifier);
void arm_split_rifft_f32(
    float32_t* pSrc,
    uint32_t fftLen,
    float32_t* pATable,
    float32_t* pBTable,
    float32_t* pDst,
    uint32_t modifier);

/**
 * @addtogroup RFFT_RIFFT
 * @{
 */

/**
 * @brief Processing function for the floating-point RFFT/RIFFT.
 * @param[in]  *S    points to an instance of the floating-point RFFT/RIFFT structure.
 * @param[in]  *pSrc points to the input buffer.
 * @param[out] *pDst points to the output buffer.
 * @return none.
 */

void arm_rfft_f32(
    const arm_rfft_instance_f32* S,
    float32_t* pSrc,
    float32_t* pDst)
{
	const arm_cfft_radix4_instance_f32* S_CFFT = S->pCfft;


	/* Calculation of Real IFFT of input */
	if(S->ifftFlagR == 1u) {
		/*  Real IFFT core process */
		arm_split_rifft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
		                    S->pTwiddleBReal, pDst, S->twidCoefRModifier);


		/* Complex radix-4 IFFT process */
		arm_radix4_butterfly_inverse_f32(pDst, S_CFFT->fftLen,
		                                 S_CFFT->pTwiddle,
		                                 S_CFFT->twidCoefModifier,
		                                 S_CFFT->onebyfftLen);

		/* Bit reversal process */
		if(S->bitReverseFlagR == 1u) {
			arm_bitreversal_f32(pDst, S_CFFT->fftLen,
			                    S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
		}
	} else {

		/* Calculation of RFFT of input */

		/* Complex radix-4 FFT process */
		arm_radix4_butterfly_f32(pSrc, S_CFFT->fftLen,
		                         S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);

		/* Bit reversal process */
		if(S->bitReverseFlagR == 1u) {
			arm_bitreversal_f32(pSrc, S_CFFT->fftLen,
			                    S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
		}


		/*  Real FFT core process */
		arm_split_rfft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
		                   S->pTwiddleBReal, pDst, S->twidCoefRModifier);
	}

}

/**
   * @} end of RFFT_RIFFT group
   */

/**
 * @brief  Core Real FFT process
 * @param[in]   *pSrc 				points to the input buffer.
 * @param[in]   fftLen  			length of FFT.
 * @param[in]   *pATable 			points to the twiddle Coef A buffer.
 * @param[in]   *pBTable 			points to the twiddle Coef B buffer.
 * @param[out]  *pDst 				points to the output buffer.
 * @param[in]   modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
 * @return none.
 */

void arm_split_rfft_f32(
    float32_t* pSrc,
    uint32_t fftLen,
    float32_t* pATable,
    float32_t* pBTable,
    float32_t* pDst,
    uint32_t modifier)
{
	uint32_t i;                                    /* Loop Counter */
	float32_t outR, outI;                          /* Temporary variables for output */
	float32_t* pCoefA, *pCoefB;                    /* Temporary pointers for twiddle factors */
	float32_t CoefA1, CoefA2, CoefB1;              /* Temporary variables for twiddle coefficients */
	float32_t* pDst1 = &pDst[2], *pDst2 = &pDst[(4u * fftLen) - 1u];      /* temp pointers for output buffer */
	float32_t* pSrc1 = &pSrc[2], *pSrc2 = &pSrc[(2u * fftLen) - 1u];      /* temp pointers for input buffer */

	/* Init coefficient pointers */
	pCoefA = &pATable[modifier * 2u];
	pCoefB = &pBTable[modifier * 2u];

	i = fftLen - 1u;

	while(i > 0u) {
		/*
		   outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]
		   + pSrc[2 * n - 2 * i] * pBTable[2 * i] +
		   pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
		 */

		/* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +
		   pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
		   pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */

		/* read pATable[2 * i] */
		CoefA1 = *pCoefA++;
		/* pATable[2 * i + 1] */
		CoefA2 = *pCoefA;

		/* pSrc[2 * i] * pATable[2 * i] */
		outR = *pSrc1 * CoefA1;
		/* pSrc[2 * i] * CoefA2 */
		outI = *pSrc1++ * CoefA2;

		/* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
		outR -= (*pSrc1 + *pSrc2) * CoefA2;
		/* pSrc[2 * i + 1] * CoefA1 */
		outI += *pSrc1++ * CoefA1;

		CoefB1 = *pCoefB;

		/* pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
		outI -= *pSrc2-- * CoefB1;
		/* pSrc[2 * fftLen - 2 * i] * CoefA2 */
		outI -= *pSrc2 * CoefA2;

		/* pSrc[2 * fftLen - 2 * i] * CoefB1 */
		outR += *pSrc2-- * CoefB1;

		/* write output */
		*pDst1++ = outR;
		*pDst1++ = outI;

		/* write complex conjugate output */
		*pDst2-- = -outI;
		*pDst2-- = outR;

		/* update coefficient pointer */
		pCoefB = pCoefB + (modifier * 2u);
		pCoefA = pCoefA + ((modifier * 2u) - 1u);

		i--;

	}

	pDst[2u * fftLen] = pSrc[0] - pSrc[1];
	pDst[(2u * fftLen) + 1u] = 0.0f;

	pDst[0] = pSrc[0] + pSrc[1];
	pDst[1] = 0.0f;

}


/**
 * @brief  Core Real IFFT process
 * @param[in]   *pSrc 				points to the input buffer.
 * @param[in]   fftLen  			length of FFT.
 * @param[in]   *pATable 			points to the twiddle Coef A buffer.
 * @param[in]   *pBTable 			points to the twiddle Coef B buffer.
 * @param[out]  *pDst 				points to the output buffer.
 * @param[in]   modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
 * @return none.
 */

void arm_split_rifft_f32(
    float32_t* pSrc,
    uint32_t fftLen,
    float32_t* pATable,
    float32_t* pBTable,
    float32_t* pDst,
    uint32_t modifier)
{
	float32_t outR, outI;                          /* Temporary variables for output */
	float32_t* pCoefA, *pCoefB;                    /* Temporary pointers for twiddle factors */
	float32_t CoefA1, CoefA2, CoefB1;              /* Temporary variables for twiddle coefficients */
	float32_t* pSrc1 = &pSrc[0], *pSrc2 = &pSrc[(2u * fftLen) + 1u];

	pCoefA = &pATable[0];
	pCoefB = &pBTable[0];

	while(fftLen > 0u) {
		/*
		   outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +
		   pIn[2 * n - 2 * i] * pBTable[2 * i] -
		   pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);

		   outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -
		   pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
		   pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);

		 */

		CoefA1 = *pCoefA++;
		CoefA2 = *pCoefA;

		/* outR = (pSrc[2 * i] * CoefA1 */
		outR = *pSrc1 * CoefA1;

		/* - pSrc[2 * i] * CoefA2 */
		outI = -(*pSrc1++) * CoefA2;

		/* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
		outR += (*pSrc1 + *pSrc2) * CoefA2;

		/* pSrc[2 * i + 1] * CoefA1 */
		outI += (*pSrc1++) * CoefA1;

		CoefB1 = *pCoefB;

		/* - pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
		outI -= *pSrc2-- * CoefB1;

		/* pSrc[2 * fftLen - 2 * i] * CoefB1 */
		outR += *pSrc2 * CoefB1;

		/* pSrc[2 * fftLen - 2 * i] * CoefA2 */
		outI += *pSrc2-- * CoefA2;

		/* write output */
		*pDst++ = outR;
		*pDst++ = outI;

		/* update coefficient pointer */
		pCoefB = pCoefB + (modifier * 2u);
		pCoefA = pCoefA + ((modifier * 2u) - 1u);

		/* Decrement loop count */
		fftLen--;
	}

}
